Waves in Dark Matter

This
is a new article reviewing a lot of old work but it also introduces some new
theory and experimental results. For example: the idea that plant frequencies
are equal in every direction is presented. This result came from calculations
of velocity ratios at different angles in plants. Rotation of live wood samples
in a vertical plane and the changes in output due to standing wave changes is
included here.

This paper
presents data that lead to the conclusion that waves are a major factor in plant
growth and that the waves interact with and are referenced to gravity. The observed
waves behave somewhat like sound waves in resonant tubes with standing waves
indicated by discretely spaced relatively wide charge locations on short blocks
cut from live trees. Apparently plant internodal spacings are related to these
charge spacings and analyses of thousands of plant-spacing measurements indicate
that internode spacings do demonstrate wave involvement by their harmonic behavior.
Electronic measurements confirm the wave frequencies. Angles that branches make
with the horizontal or vertical appear to be predominately integral multiple
of five degrees. The growth of reaction wood tends to confirm this effect. The
data demonstrate that vertical wave velocities are generally greater than horizontal
velocities by integral multiples of some basic velocity. The wave velocity seems
to increase in steps from the horizontal to the vertical. This suggests that
discrete charge locations move apart when a branch section is tipped from the
horizontal to the vertical. Sinusoidal voltages from two probes on shielded
live branch sections rotating in a vertical plane confirm this effect. Internodal
spacings get larger on average, due to increasing wave velocity, as the angles
that a branch makes with the horizontal increases in steps to the vertical.
Fiber cells often get longer in a similar manner. Spacings converted to frequency
and branch angles demonstrate wave behavior, and gravity interaction. The vertical
to horizontal velocity ratios and the measurement of velocities indicate wave
involvement related to gravity. The data confirming wave behavior connected
with gravity appear to be unlimited. The waves demonstrated here might be some
type of gravity waves, since they are obviously referenced to and otherwise
tied to gravity.

Some details
are understood on how a plant responds to gravity but it is still not well understood
how whole plants respond to gravity (Salisbury 1993 and Fern, Wagstaff, and
Digby 2000). For more than 25 years I have, as a physicist, have been making
electrical measurements on plants. For about ten years I used probe pairs. After
discovering waves in 1988, I used many probes often near a half wavelength apart.
I measured many thousands of internodal spacings and angles of growth of trunks,
branches, and their components. I found that plants of all measured species
seem to be limited in the spacings and growth angles that are allowed, and these
seem to repeat from plant to plant and species to species. There appear to be
some very dominant spacings representing dominant frequencies as indicated by
peaks on distributions. Actual measurement of frequencies on a spectrum analyzer
indicated large amplitude signals for the dominant frequencies corresponding
to the dominant spacings. Angles of growth appear to be mostly limited to integral
multiples of about 5 degrees away from the horizontal in the species measured
at least for the smaller angles. Horizontal spacings are usually the smallest
on average but internodal spacing averages, (and often cell lengths) apparently
increase in steps as the angle with the horizontal increases. The different
velocities of waves in plants appear to control the latter behavior. The velocity
of the waves apparently increases in steps thus increasing the spacings. This
behavior suggests quantization. Quantization (in this case repetition of charge
piles, incremental angles from the horizontal, a limited number of internodal
spacings, or step changes in velocity) is often found in physics and my published
data indicate that plants follow their own specialized quantization rules related
to gravity. Quantization generally means that standing waves are involved. The
waves discussed here seem to be governed by the rule for simple waves that velocity
equals frequency times wavelength v=fλ.For
example, obtaining a velocity and an internodal spacing (most often considered
a half wavelength in this article) gives me two of the variables in the latter
equation and so a frequency can then be calculated.

Waves
are found everywhere. For example, all matter is largely made with standing
quantum waves. Crystals are formed by standing waves (see physics texts). It
is only natural that plants should utilize waves. Apparently, there is a set
of many different frequencies of standing waves in plants with their corresponding
half wavelengths. When the tip of a branch starts to grow at a bud in the spring,
I assume it starts at a node and stops at an ending node, a half wavelength
of a permitted frequency in the plant. The chosen permitted half wavelength
is determined by the growing conditions. Internodal spacings are aptly named.
When I first found wave in plants, I found charges piled at intervals along
peeled tree trunks. These charge piles were wide and tapered off at the ends,
as one would expect for standing waves (Fig. 1).

Figure 1. Variation in voltage
from a probe going up a Pacific Madrone sample quickly cut out from a longer
sample. Not that the spacings are quite close to equal even though probe characteristics
tend to cause errors. The results from this type of sample suggested to me
that standing waves with shorter wavelengths than in the originating tree
built up within a few minutes from cutting out the sample. A reference probe
was placed in the bottom of the sample while a second probe was used to measure
up the sample. This graph is from 1988 data used in Wagner 2001 and used by
permission of Frontier Perspectives.

Regular intervals are observed only under the
proper conditions because there are many frequencies in a plant represented
by different spacings. I quickly cut sections out of the small trees, and it
appeared that the charge concentration locations at least partially telescoped
into the short sections. It was near 0o Celsius when I did these
first experiments. The low temperature may have helped eliminate some of the
many frequencies and therefore spacings. I was thus often able to find simple
resonant patterns. These waves might be special gravity waves since they seem
to be so closely intertwined with gravity as will be pointed out later. I have
been trying for years to reproduce and measure them in the laboratory with considerable
success. In 1988, I called them W-waves because they were first found in wood.
The experimental evidence indicates that they are longitudinal waves because
branch spacings and thus half wavelengths are often much larger than very small
trunk or stem diameters. Transverse waves need room for vibration perpendicular
to the direction of travel.

Workers have been using probes in plants for
many years. Much of the work was started by Bose (Bose 1907) and was continued
by other workers such as Fensom (1964, 1985), Gensler (1974), Lund (1947), and
Raber (1933). I used probes in plants for around 10 years before I stumbled
onto the wave characteristics in 1988. I concluded that most of my early two-probe
work was not revealing anything very important. One could relate some of the
electrical curves obtained to plant characteristics but it appeared that much
of the work was not repeatable (Wagner 1988 and Raber 1933). Not until multi-probing
seemed to indicate wave characteristics did I become really excited. The later
work and waves explained the non-repeatability of my early work. Much of the
early work of others (e.g. Janick (1993)) appeared to be related to what were
called action potentials, not of single cells as often defined but having to
do with signals traveling along stems. Their work appears to be related to my
measurements of wave velocities. I attempted to calculate the velocities of
the signals involved in the Janick reference Figure 19-4 (Janick 1993) by methods
I use in my work but the electrode spacings were not given. Otherwise the curves
in the figure look like ones that I use in measuring wave velocities. My mearurements
indicating standing waves don't appear to be directly related to action potentials.

Materials and Methods

Most of
the data reported herein are from the following species: Grand fir (Abies
grandis (Dougl.) Lindl), Douglas fir (Pseudotsuga menziesii
(Mirb.) Franco), Red alder (Alnus rubra (Bong)), Big leaf maple (Acer
macrophyllum Pursh.), Golden weeping willow (Salix sp. L.), False
indigo (Amorpha fruiticosa), Delicious apple (Malus sp. Mill),
Weeping birch (Betula sp. L.), Golden chinkapin (Castinopis chrsophylla
(Dougl.) A. DC.), Ponderosa pine (Pinus ponderosa Laws), Hind's willow
(Salix sp. L.), Incense cedar (Libocedrus decurrens Torr.), and
Pacific madrone (Arbutus menziesii Pursh.). For electrical measurements,
I used sharp top insulated steel probes (usually #2 steel pins) connected through
high resistances (about ten megohms) to a high input impedance millivoltmeter.
In the beginning a reference probe was placed in the bottom of the sample. In
the initial work a second probe was quickly pushed in two millimeters or so,
a reading recorded and then the probe was pulled out, and then pushed in farther
along (usually up as in the plant) the sample and so on. Care was taken to prevent
human body influences on the readings by using probes that were highly insulated
from one's hands. Readings, when plant waves were discovered, were taken at
about 0o C in January 1988 (Wagner 1988). I quickly peeled the bark
from the first samples. These peeled samples seemed to put out data for only
about 25 minutes. Later I just removed the bark from the probed area when the
readings didn't have to be taken so quickly or over a continuous area, such
as for longer term measurements along a tree trunk. The spacing and angle measurements
were taken using a centimeter rule and a #36 Polycast protractor (essentially
a hanging weight with a scale; which can measure to about 0.25 degree). Angles
were measured on branches of plants that were straight for at least four branch
diameters. These straight portions were generally close to the trunk of a tree.

Velocities
of waves in trees were measured by very fast wounding at one point on the plant
and then recording and analyzing the resulting electrical signal from two probes
placed as far apart as possible above the wounding point or farther out on a
branch. The rise time (the initial straight line portion of a recorded curve)
was considered the time the signal traveled between the two probes (Wagner 1996
and the Janick figure). Note that the rise time may appear longer than it should
if the wounding pulse is not made fast enough.. The method used here has been
checked many times using known distances and tree heights. One has to be careful
about reflections from branches (Wagner 1988, 1996, & 2001). In the case
of the sugar pine of Table 1, most of a small tree was brought into the lab
and the vertical velocity was measured standing the tree upright and the horizontal
velocity measured with the tree trunk level. Signal probes were two meters apart
on the sugar pine and the measuring signal recorded on a strip chart recorder.
Frequencies of the waves were measured on a Schlumberger 1201 spectrum analyzer
(Wagner 1989, 1990-).

Measurements were taken from rotating 40 cm
live samples (approx. 1 cm in diameter) in an aluminum box by taking bark off
small areas near the ends to place probes (Fig 4). Leads from the probes carried
the output through a plastic pipe that held and rotated the sample, to a strip
chart recorder outside the aluminum box. The coaxial leads were made long enough
so they could wind up on the plastic pipe as the pipe made one full rotation
once every 16 minutes driven by a geared down motor. The leads were unwound
for the next reading.

RESULTS AND DISCUSSION

Charge and Plant Spacings

In January 1988, I observed, using steel probes,
that negative charge seemed to pile up at regular relatively large intervals,
as indicated by probing, along quickly peeled small tree trunks. I then cut
blocks out of small trees and quickly (within a minute) peeled and probed them.
In this case, much closer spacings between charge piles were observed. The charged
areas were wide as one would expect for standing waves.(Wagner 2001) (Fig. 1.)
These areas developed within a few minutes (approx. 10 min) in the short blocks
and then they quickly died out (within about 25 minutes) probably because these
early samples were peeled. The charge spacings seemed to telescope after the
blocks were cut out like sound wavelengths in a resonating sound tube when it
is shortened. These shorter spacings apparently represent higher resonant frequencies
(Wagner 1988, 2001). In 1988, I was first unaware that the blocks should have
been of specific lengths, determined by the wavelengths of permitted dominant
frequencies. This would have maximized the results due to resonance at a particular
frequency, if the sample is an integral multiple of a half wavelength long.
I probed so many samples that the effect finally became obvious even though
with many samples the spacings weren't evenly spaced because more than one frequency
was present. The low temperature at the time of the early measurements (near
0o C) may have limited the observed frequencies and facilitated finding
repeating spacings. I concluded that plant internodal spacings are related to
the early negative charge spacing observations and are also quantized. The regular
repeating spacings suggested standing waves. The waves seemed to be reflecting
back and forth in the freshly cut samples building up a standing wave indicated
by repeating charge piles observed within a few minutes from cutting. I assumed
these charge piles were related to plant nodes. So the measurement of many thousands
of internodal spacings began. I most often called these spacings half wavelengths
of standing waves (Wagner 1990)with different spacings representing
different frequencies in the plant. Actual measurement of frequencies of the
waves confirm that the waves are real. I used a Sclumberger 1201 spectrum analyzer
to measure frequencies for several years in the initial work to be sure that
waves were being observed? (Wagner 1989, 1990). Actual measurements gave me
the data so that I could label the frequency peaks in the published frequency
distributions. I spent much of the time in my early work actually measuring
frequencies of the waves. I observed larger amplitude signals at certain frequencies
and their harmonics that seemed to be associated with the largest peaks (more
spacings) found in distributions of plant spacings (Figs 2,3).

Note that the distributions are not smooth
curves but show discrete peaks with apparently a limited number of frequencies.
In the given figures the same velocity (96 cm/s) was used to calculate the frequencies
from internodal spacings so the vertical and horizontal distributions appear
to have different frequencies by a factor of 2 from a quick visual comparison
of? Figures 2 and 3. Later work indicates that the apparent difference in frequencies
is due to different velocities with the vertical velocities apparently greater
than the horizontal by a factor of near 2 on average for the many species shown
in these two distributions. The distributions and frequency measurements leave
little doubt that waves are involved. Other measurements continue the proof
(see all the Wagner references). Note that if a particular frequency actually
had a higher velocity than 96 cm/s as was used in obtaining the two graphs shown
it would appear as a higher frequency multiplied by an integral factor since
velocities appear to be integral multiples of a basic velocity.

Not only
do live samples show the charge spacing effect but also samples soaked in saturated
salt solution and partially dried develop similar, but much weaker (indicated
by lower voltages from probing), charge piles (Wagner 1989). Note that ordinary
porous materials don't show these charge spacings. There seems to be some electronic
characteristics very special about the plant xylem structure that separates
it from ordinary porous substances (Wagner and Deeds 1968). Studying salts in
plant material first sparked my interest in studying live plant material. There
is a whole list of special electrical characteristics that set it apart (mostly
unpublished work). For example if one places steel probes near the ends of one
of these samples and connects them to a high impedance voltmeter, one can often
observe a change in the output voltage as one changes the sample orientation
from upright to horizontal or vice versa. Also, if ac current is run through
a salt filled wood sample the end that was lower
in the tree heats up while the upper end remains cool (unpublished).

Figure 3. For this frequency distribution
I used vertical spacings from prickly lettuce (Lactuca serriola), sweet
corn (Zea mays saccarata), branch whorls from ponderosa pine, big leaf
maple, delicious apple, red alder, weeping flowering cherry, golden chinkapin,
Dutch elm, false indigo, Hind's willow, and weeping willow. I used 96 cm/s for
the velocity to calculate the frequencies for comparison purposes. Actual velocities
were often integral multiples of 96cm/s which would make many of the frequencies
much higher using velocity equals frequency times wavelength. At the time the
data were taken the larger velocities had not been measured. Spectrum analyzer
data indicated frequencies of higher multiples were present.

Much
of the same was found true for live samples where one removed a little bark
to place the probes. The orientation effects can be attributed to charge location
changes. The velocity for the waves apparently increases, due to increasing
gravity, when one changes the sample orientation from horizontal to vertical,
but the frequencies remain the same. The charge concentrations are farther apart
because the wave velocity becomes larger. This suggests that the spacings between
charge locations increase as the sample orientation is changed from horizontal
to vertical. I slowly rotated several both live and salt filled samples in a
vertical plane in a grounded aluminum box. A typical curve that resulted (for
a 40 cm live sugar pine sample about 1 cm in diameter) is shown in Figure 4.
This is another demonstration of wave behavior.

Figure
4. Output from two probes near the ends of a 40 cm live sugar pine sample
rotated in a vertical plane in a grounded aluminum box. The peak output voltage
was about 1.75 mv on top of a steady voltage of near 5 mv. The period of rotation
or the peak-to-peak time is 16 minutes to permit time for the charge locations
to readjust. This result was just a typical curve of several rotated live
samples. The output voltage from salt filled samples was generally near half
that of live samples. As a control a sample was rotated in a horizontal plane
with the resulting output a straight line.

Velocity
Increases as the Angle with the Horizontal Increases

It was found that vertical
velocities are usually larger than horizontal velocities by a factor of a ratio
of small integers. This is confirmed by the following results from the species
of trees and bushes listed in Table 1. I measured spacings that were both vertical
and horizontal for each of the given species. I then took reciprocals of these
spacings and took averages of each set of these reciprocals to obtain the averages
Av and Ah. Note that each of these (averages) reciprocals
multiplied by a velocity is a frequency considering that the spacings are ½
wavelength long. I then equated each vertical average multiplied by the vertical
velocity vv to its corresponding horizontal average multiplied by
the horizontal velocity vh since it is only reasonable that vertical
and horizontal frequencies are the same and experiment bears it out (note that
the factor of 2 due to half wavelengths divides out). So one has the equation
vvAv=vhAh for each species. This
can be written vv/vh=Ah/Av. It turns
out that these ratios are generally found to be ratios of small integers, which
one would expect if one were dealing with ratios of two velocities that are
integral multiples of a basic velocity. In March of 2005, I measured horizontal
and vertical pairs of velocities from three species of trees. These species
were sugar pine, Ponderosa pine, and incense cedar. The actual velocity ratios
found were those predicted by the ratios derived from spacings for two of the
species. Sugar pine branch spacings and cell lengths had not been measured.
See Table 1.

The increase in charge spacings
provides the plant a way to differentiate between horizontal and vertical. This
provides a reason for the plant to produce hormones to increase the vertical
internode lengths to fit with the increased wavelengths and provide for the
design of the tree or other plant. It appears that a plant's structure or plant's
genotype determines which velocity ratio appears, as 2/1 in sugar pine, 4/3
in apple, and others. Differences between the integral ratios and the calculated
values were less than 1% on average. Note that the velocity ratios indicate
the shape of the tree or bush.

Available measurements
of velocity apparently indicate integral multiples of 96 cm/s and sometimes
integral multiples of 48 cm/s during the growing season. A low bush might have
a velocity ratio of 144/96. For example apple (ratio 4/3) tends to be a short
chunky tree while ponderosa pine (ratio 3/1) is tall and spindly. Most of the
given ratios are for short wide type trees or bushes. Of course the trees tend
to grow differently in different light intensities in which case the plant requires
different spacings of the available pool. This goes along with the idea that
growing conditions determine the spacings and thus the chosen frequencies.

I also measured thousands
of vertical and horizontal fiber lengths from tree tissue with similar ratios
except that fiber lengths represent much higher frequencies. Some cell ratios
were near 1/1 while other ratios apparently represent velocity ratios (Wagner
1999a). Sometimes it appears that branches have been bent down and uncorrected
by the plant after fiber formation so the angle is incorrect. Care was taken
to avoid the latter.

TABLE I. Results of measurements of
vertical (V) and horizontal (H) branch and leaf spacings on trees. Also thousands
of cell lengths from vertical and horizontal portions were measured and analyzed.
Normally I took averages of the reciprocals of the spacings and cell lengths.
When these averages are multiplied by a velocity they represent frequencies
and one equates frequencies to find the velocity ratio. See the text. Vertical
and horizontal velocities are being measured. Three sets are given here. Horizontal/vertical
needles per unit length are given for sugar pine.

Consider incense cedar where it appears that the corresponding
ratios for fibers indicate the shape of the tree. In other words, it appears
that much higher frequencies (wavelengths of cell lengths instead of plant
internode lengths) indicate the shape of the plant. On incense cedar, the
branches often appear to be almost randomly placed, but the cell ratios seem
to show the shape of the tree and a velocity ratio. Actual velocity measurements
indicate the latter is the case. For incense cedar for the horizontal, I measured
369 cell lengths.At 45o from the horizontal, I measured 336 lengths,
and for the vertical 320 lengths. Note an apparent 5o rulefor fiber lengths. So in the case of incense cedar much higher frequencies
(calling cell lengths half wavelengths) indicate the shape of the tree with
vvAv=v45A45=vhAh
(the frequencies are equal for every angle). The ratio derived from
cell lengths vv/vh for incense cedar was 8/3 (actual
from fiber lengths ratio 2.57). This compares favorably with the measured
velocity ratio. See Table 1.

Another interesting tree is Pacific madrone. The branch
spacings appear rather random and slope angles are hard to read because of
the bumpiness of the tree surface. Here I measured fiber lengths from samples
with growth angles of 0o, 45o, 65o, and 80o
from the horizontal. The numbers of fibers measured were 342, 330, 367 and
341 respectively. The simple ratio vv/vh=9/5 (1.80 was
the actual figure found) was found by extrapolation to the vertical using
the 5o rule with the equation vhAh=v45A45=v65A65=v80A80=vvAv.

The standard
deviations for all the above averages ranged between 15 % and 45 % of the calculated
averages. Many other trees and other plants were measured, but the above were
chosen for typical examples of quantization with respect to the gravitational
field. I made similar measurements on non-trees (e.g. prickly lettuce (Lactuca
serriola L.) and sweet corn ) and obtained similar results. The internodal
spacings are again quantized and apparently come from the general pool. These
latter and other similar plants were not studied to the extent of the given
trees and bushes reported in this article.

Another
very simple possible approach to find velocity ratios on some trees like ponderosa
pine is to analyze the most recent growth for the velocity ratio. For example,
find the number of needles per unit length for vertical and horizontal from
the top of a small Ponderosa pine tree and take the ratio of horizontal to vertical
for a ratio of 3/1, or 2/1 for sugar pine.

When I
first began my plant work, I was unaware that vertical velocities are usually
larger than horizontal velocities and that there were multiple velocities. I
used one initial measured velocity (96 cm/s which is still much faster than
ionic diffusion velocities) for my initial calculations of frequency. I often
graphed the number of spacings at all angles as the ordinate versus frequency
as the abscissa. These graphs indicate that certain frequencies are predominant
and that observed frequencies and thus certain spacings are predominant. The
early graphs, however, still indicate the wave nature even though likely most
of the frequencies were too low and should have been multiplied by integers
like 2, 3, 4, 5, etc. The graphs still indicated that the frequencies are generally
harmonics (integral multiples) of some lower basic frequency and that vertical
and horizontal frequencies were similarly related. The early graphs indicate
that frequencies (which were verified with a spectrum analyzer) and spacings
repeat from species to species. Thus the wave nature of plants was proved at
the start of the research (Wagner 1990, 1999a). I want to emphasize again that
nutrition, temperature, and water available as well as other conditions determine
a particular internodal spacing. There apparently is a limited pool of spacings
from which the choice is made, however.

The wave velocity apparently increases slowly at first
from the horizontal and rises more rapidly as the growth angle approaches
the vertical. I found this from cell length data and other observations of
plants. For example see Wagner (1999a), Table III, and correct for the 96
cm/s and use the idea that frequencies are equal at all angles.

Quantized
Growth Angles

I
measured angles that branches made with the horizontal and found them to be
predominantly near multiples of five degrees from the horizontal or vertical
thus finding that plant growth angles tend to be quantized (Wagner 1997, 1999a)with respect to the gravitational field. For example, angles with the
horizontal were measured for branches on big leaf maple: 299 angles were measured.
198 angles were right on integral multiples of 5o as best as could
be measured with the protractor. 53 angles were within 1 degree off
from 5o degree multiples. 48 angles were further off than 1o
from an integral multiple of 5o. These results look very good due
to the roughness of surfaces, disturbance of the branch on measurement, and
other possible variables such as an angle that the plant has not corrected.
If the angles were random the numbers would have been 62 at 5o multiples,
118 angles would have been within one degree away from a multiple of 5o,
and 115 more than one degree away from a multiple of 5o (zero is
considered an angle here). Douglas fir provided 239 angles: the corresponding
numbers are 114, 52, and 73 respectively (random 50, 95, 92). Red alder gave
335 angles with the numbers 232, 55,48 respectively (random 69, 132,129). Six
other species around the laboratory provided 114 angles. The corresponding numbers
are 80,22,12 respectively (random 24,45,44). From this kind of data it was concluded
that growth angles tend to be quantized at integral multiples of 5ofrom
the horizontal for many species at least for the smaller angles. The angles
were distributed with more angles at the lower multiples of 5o (See
Wagner 1997, 1999a for plotted distributions). The results given here are typical
examples. Tree branch angles both above and below the horizontal seem to be
specified by the 5-degree rule discussed above. The 5o quantized
branch angles help explain the growth of reaction wood a tree grows to correct
artificially changed branch angles (Salisbury and Ross 1985). This is also excellent
evidence for the wave model.

DISCUSSION

A summary
of some of the evidences that waves have much to do with plant operation is
as follows:

(1) The
placement of charge concentrations on the samples tested (Wagner 1988).

(2) Extensive
measurement of plant frequencies with a low frequency spectrum analyzer. These
measurements were both direct and by the use of beat frequencies where I applied
a reference signal to the tree. (e.g.Wagner 1989, 1990.)

(3) The
discrete organization of plant internode spacings as shown in Figures 2 and
3 for example.

(4) The
behavior of plant internodal spacings growing in the presence of high voltage
ac line electric fields. Some shorter plant internodal spacings seem to be nearly
eliminated. It appears that the frequencies connected with these particular
internodal spacings are close to line frequencies, which seems to prevent their
growth is my hypotheses. The longer internode spacings appeared to become more
dominant in the presence of the electric fields (Wagner 1995b, 2001).

(5) Measurement
of the gravitational field within small holes in the xylem, using tiny accelerometers
(and hanging weights in vertical holes in leaning trees) seemed to indicate
a reduction in the gravitational field in vertical trunks of up to 25 % at near
maximum sap flow. Also forces were measured in horizontal roots, which indicated
assistance to sap flow. I attributed these forces initially to moving standing
waves producing the forces. The gravity like forces measured apparently were
just a small indication of the real gravity like forces involved because of
the disturbance of the plant tissue in placing tiny measuring accelerometers.
(Wagner 1991, 1995a) The brass shielding of the accelerometers and the distance
of the accelerometer from the tree tissue indicated that the forces were gravity
like and not Casimir or Van der Waals forces.

(6) The
slope of branches at apparent predominant angles of integral multiples of 5o
(Wagner 1997).

(7) The
sending of signals to surrounding trees indicating that the transmitting tree
had been wounded (Wagner 1989)

It appears
that there is a set of rules related to the gravitational field that constrain
the plant. The described mechanisms may be all that is necessary to add to present
theory to explain a plants response to gravity. Apparently, plant genotypes
determine the velocities and velocity ratios while growing conditions predominantly
determine the frequencies or spacings chosen from the available pool. Some special
conditions apparently change the rules. It is likely that waves from different
plants interact. For example, I found altered velocity ratios in shorter trees
growing under taller trees where the sun provided nearly equal lighting to both
trees. The vertical data seemed to lessen the velocity ratio to a lower value
in the trees growing under taller ones (unpublished). There may be velocity
ratios that are less than or equal to one and possibly different basic velocities
than the ones given. Data indicate that velocities may be different during different
seasons. Perhaps the wave velocity increases in steps from the horizontal to
the vertical with each 5o interval representing a step with spacings
increasing accordingly. The given results together with previous findings then
seem to indicate how whole trees and bushes respond to gravity. It appears that
new growth, at the end of a branch, stops at the far node of a particular half
wavelength (represented by a particular frequency and a velocity for that particular
angle from the horizontal) determined by growing conditions. The data given
here may imply that there may be an all-inclusive law, related to quantum mechanics,
for plant growth that can be written as a simple equation or set of equations.

One of
the best other evidences for the wave theory is the growth of reaction wood
to correct a plant growth angle (Salisbury and Ross 1985) indicating that a
plant part is "tuned" to a particular angle of growth. The averages
derived from plant spacings and fiber lengths had large standard deviations
(in the range of 15% to 45% of the averages obtained). The large standard deviations,
where the spacing data is taken from several different plants to obtain a good
sampling, and the simple velocity ratios that are, on average, within 1% of
ratios of small integers constitutes mathematical proof that frequencies are
the same at all angles and that the wave theory is correct. It reminds one of
ordinary quantum mechanics where one takes averages to come up with exact characteristic
quantities. Other proofs of the wave theory include actual measurement of the
wave velocities and observing that the number of frequencies available to plants,
although large, seem to be limited to specific values. These values seem to
be harmonically related to one another (i.e. they seem to be integral multiples
of more basic frequencies), which again indicates waves. See especially my earlier
literature starting in 1988 for actual measured values of frequencies that indicate
harmonic behavior. At first, I was unaware that velocities vary by integral
multiples so the early published frequencies often need to be multiplied by
2 or 3 or 4 or maybe 5 or more and so on. The integral multiple and other wave
characteristics are still evident, however. I did much more work than is indicated
here. For example, as mentioned earlier, I measured relatively large gravity
like forces associated with sap flow within xylem tissue (Wagner 1991, 1995a.).
These forces tend to belie the usual theory of sap flow. I found that there
seems to be a high energy density in xylem tissue associated with the waves
in plants (Wagner 1993). I obtained up to 8 volts from polyethylene shielded
silicon pn junctions placed in dark horizontal slits in trees. These might even
be used as power sources with proper modification I also tried many approaches
to these waves attempting to make them useful external to plants. For more details
see the references, my web site, and other publications.

Note that
the velocities of the observed plant waves both inside and outside of plants
may suggest that some other than the commonly found wave medium is involved.
I hypothesized that dark matter might be involved. Dark matter is everywhere
and composes most of the mass of the universe. I wrote two documents using this
hypothesis. Here I calculated that the wave velocities that I found in dark
matter were comparable to the velocities that I found both inside and outside
of plants (Wagner 1995 and Wagner 1999).

Acknowledgement:
I thank my wife Claudia for reading the manuscript and making comments.